# What are the mean and standard deviation of {115, 89, 230, -12, 1700}?

Apr 16, 2018

Arithmetic Mean $\approx 424.4$

Standard Deviation $\approx 642.44$

#### Explanation:

Input Data Set: $\left\{115 , 89 , 230 , - 12 , 1700\right\}$

Arithmetic Mean $= \left(\frac{1}{n}\right) \cdot \Sigma \left({x}_{i}\right)$,

where, $\Sigma {x}_{i}$ refers to the Sum of all the elements in the Input Data Set.

$n$ is the total number of elements.

Standard Deviation $\sigma = \sqrt{\frac{1}{n} \cdot \Sigma {\left({x}_{i} - \overline{x}\right)}^{2}}$

$\Sigma {\left({x}_{i} - \overline{x}\right)}^{2}$ refers to the average of the squared differences from the Mean

Make a table of values as shown:

Hence,

Arithmetic Mean $\approx 424.4$

Standard Deviation $\approx 642.44$

Hope it helps.